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Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry.

Antoine Diez1, Andrew L Krause2, Philip K Maini3

  • 1Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University Institute for Advanced Study (KUIAS), Kyoto University, Yoshida-Konoe-cho, Sakyo-ku, Kyoto, 606-8501, Japan.

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|January 3, 2024
PubMed
Summary

This study explores Turing patterning in stratified biological tissues, considering reaction-cross-diffusion models. Findings reveal how tissue layer coupling can induce or prevent pattern formation, impacting biological self-organization.

Keywords:
ChemotaxisInterfaceSkin patternsStratified systemsTuring instabilities

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Area of Science:

  • Mathematical Biology
  • Developmental Biology
  • Biophysics

Background:

  • Turing's mechanism explains self-organization via reaction-diffusion systems.
  • Tissue stratification, common in embryonic skin, involves distinct layers with unique biochemical processes.
  • The impact of tissue stratification on Turing patterning remains under-explored.

Purpose of the Study:

  • To investigate Turing patterning conditions in bilayered reaction-cross-diffusion systems.
  • To analyze the role of differential interfacial transport and layer asymmetry.
  • To quantify patterning conditions in stratified biological tissues.

Main Methods:

  • Theoretical analysis of reaction-cross-diffusion models in bilayered regions.
  • Linear stability analysis around homogeneous equilibrium states.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Quantitative Turing conditions derived for arbitrary numbers of reacting species.
  • Demonstrated how interfacial transport and layer asymmetry influence pattern formation.
  • Identified scenarios where layer coupling overrides individual layer patterning states.

Conclusions:

  • Tissue stratification significantly impacts Turing patterning dynamics.
  • Interfacial coupling can act as a switch for pattern formation or stabilization.
  • The study provides a framework for understanding self-organization in complex biological structures.